Polynomial Ring over an Integral Domain Algebra Subgroups and Normal Subgroups Under Group Homomorphisms Algebra Matrix Characterisation of Bilinear Rank Algebra Existence and Uniqueness of the Fraction Field Algebra Short Exact Sequence and Chain Conditions Algebra Dynkin Diagram Determines the Finite-Type Cartan Matrix Algebra Extension Distributes Over Tensor Product Algebra First Isomorphism Theorem Group Theory Algebra Area